Journal of Convex Analysis 32 (2025), No. 4, 1045--1064
Copyright Heldermann Verlag 2025
Optimization of Elliptic Type Differential Inclusions with Mixed Boundary Conditions
Elimhan N. Mahmudov
(1) Department of Mathematics, Istanbul Technical University, Istanbul, Turkey
(2) Azerbaijan National Aviation Academy, Baku, Azerbaijan
elimhan22@yahoo.com
Dilara I. Mastaliyeva
Institute of Control Systems of the Ministry of Science and Education of the Republic of Azerbaijan, Baku, Azerbaijan
dilara.mestelieva@gmail.com
This paper first deals with the Neumann problem for discrete, discrete-approximate problems and elliptic differential inclusions. Then using the obtained results for discrete inclusions in the form of Euler-Lagrange inclusions necessary and sufficient conditions for optimality are derived for the problems under consideration. Further, these problems are generalized to mixed problems, where the Neumann and Dirichlet conditions are satisfied separately in different parts of the set-valued mapping domain. As an example, a linear optimal control problem is considered, from which the Weierstrass-Pontryagin maximum condition follows. Thus, relying only on the previous auxiliary results, we can obtain the main results of this paper for mixed problems. In turn, the Neumann problem is generalized to the multidimensional case with a second order elliptic operator.
Keywords: Discrete-approximate, elliptic differential inclusion, Neumann, Dirichlet, mixed problems, necessary and sufficient conditions.
MSC: 35J15, 47J22, 49K20.
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